A line segment is bisected by a line with the equation # 9 y + x = 5 #. If one end of the line segment is at #( 7 , 4 )#, where is the other end?

1 Answer
Jun 15, 2017

The other end is: #( 249/41,-178/41)#
Here is a graph:
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Explanation:

Given: #x+9y=5" [1]"#

The family of perpendicular lines is:

#9x-y=k#

Use the point #(7,4)# to find the value of x:

#9(7)-4=k#

#k = 59#

The equation of the bisected line is:

#9x-y=59" [2]"#

Multiply equation [2] by 9 and add to equation [1]:

#82x= 536#

#x_"midpoint" = 268/41#

Use the midpoint equation to find #x_"end"#

#x_"midpoint" = (x_"start"+x_"end")/2#

#268/41 = (7+x_"end")/2#

#x_"end" = 536/41-7#

#x_"end" = 249/41#

Find #y_"end"# by substituting #x_"end"# into equation [2]:

#9(249/41)-y_"end"=59#

#y_"end" = 9(249/41)-59#

#y_"end" = -178/41#